Configuration design of the emission control areas for coastal ships: A Stackelberg game model

Several countries and regions have announced sulphur emission control areas (SECAs) to regulate sulphur emissions from ships. Incorporating environmental benefits and economic impacts, a bi-level programming model following the Stackelberg game regime is proposed to capture the SECA design problem for a given coastal area, in which the irregular polygon of the SECA is assumed to be a convex hull and described by a system of linear constraints. The government, as the leader, minimizes total sulphur emissions of ships over the entire coastal area with the voyage cost constraint. The ships, as followers, minimize individual voyage costs by jointly choosing the sailing trajectories and speed profile inside and outside the SECA between the associated port pairs with the given geometric configuration of the SECA. We first derive the optimal trajectory and speed profile for each ship, which can be simplified to a shortest path problem. Subsequently, a heuristic algorithm based on the steepest descent method is proposed to obtain the Pareto optimal solution in the sense of simultaneous minimization of total emissions and voyage costs. Finally, two announced SECAs are adopted to illustrate the validity of the proposed model and algorithm.